up to some universal constant.
In this subsection, we aim to demonstrate the association between the length-based complexity measure (REF ) and the generalization gap. To show this, we follow [1]}, [2]} to compare the length-based measure with another 18 complexity measures (including norm-based, flatness-based and margin-based measures, see details in Appendix REF ) by calculating the Kendall’s rank coefficient [3]}.
Specifically, for a set of training processes \(\mathcal {P} = \left\lbrace p_1, p_2, \ldots , p_k\right\rbrace \)  where each \(p_i\)  corresponds to one particular training process that contains all the information of the model during training, then the Kendall's rank coefficient \(\tau _{\mathcal {P}}\)  of
a complexity measure \(\mu \)  and the generalization gap \(g\)  is given by
\(\tau _{\mathcal {P}} = \frac{\sum \limits _{i, j \in [k], i \ne j} \operatorname{sgn}\left(\mu (p_i) - \mu (p_j)\right) \operatorname{sgn}\left(g(p_i) - g(p_j)\right)}{k(k-1)},\) 
